Influence of Raman scattering on ocean color...

Influence of Raman scattering on ocean colorinversion models

Toby K. Westberry,1,* Emmanuel Boss,2 and Zhongping Lee3

1Department of Botany and Plant Pathology, Oregon State University, Corvallis, Oregon 97331-2902, USA2School of Marine Sciences, University of Maine, Orono, Maine 04469-5706, USA

3Environmental, Earth, and Ocean Sciences Department, University of Massachusetts Boston, Boston,Massachusetts 02125, USA

*Corresponding author: [email protected]

Received 18 March 2013; revised 12 June 2013; accepted 6 July 2013;posted 8 July 2013 (Doc. ID 187324); published 1 August 2013

Raman scattering can be a significant contributor to the emergent radiance spectrum from the surfaceocean. Here, we present an analytical approach to directly estimate the Raman contribution to remotesensing reflectance, and evaluate its effects on optical properties estimated from two common semianalytical inversion models. For application of the method to ocean color remote sensing, spectralirradiance products in the ultraviolet from the OMI instrument are merged with MODerate-resolutionImaging Spectroradiometer (MODIS) data in the visible. The resulting global fields of Raman-correctedoptical properties show significant differences from standard retrievals, particularly for the particulatebackscattering coefficient, bbp, where average errors in clear ocean waters are ∼50%. Given the interestin transforming bbp into biogeochemical quantities, Raman scattering must be accounted for in semianalytical inversion schemes. © 2013 Optical Society of AmericaOCIS codes: (010.4450) Oceanic optics; (010.0280) Remote sensing and sensors; (010.5630)

Radiometry; (010.1690) Color.http://dx.doi.org/10.1364/AO.52.005552

1. Introduction

Ocean color inversion models provide a means of re-lating the emergent radiance spectrum to various ab-sorbing and scattering components in the surfaceocean [1]. In turn, these absorption and scattering in-dices convey rich information on suspended and dis-solved materials that can now be estimated fromsatellite at global, synoptic scales. Some of the bettercharacterized bio-optical signals (e.g., chlorophyll orwater transparency) have been used to examine long-term changes in ocean properties associated withclimate variability [2–4]. However, the accuracy ofretrieved quantities depends upon a number offactors ranging from satellite sensor calibration to

the formulation of the inversion algorithm itself.The latter depends upon the ability to account forall significant processes affecting light transmissionand propagation in the ocean and atmosphere. Someof these processes and relationships can be expressedanalytically in an inversion algorithm, while othersrely on empirically derived information.

One such physical process that affects the ambientlight field is Raman scattering. Raman scattering is aquantum molecular phenomenon that results fromphoton interactions with the medium itself (e.g., sea-water), and which are re-emitted at wavelengths dif-fering from the excitation source [5,6]. While Ramanscattering is often conceptually lumped togetherwith other “trans-spectral” processes, it is a funda-mentally different process from other forms ofabsorption-reemission interactions, such as fluores-cence. Unlike fluorescence, Raman scatter is

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associated with a fixed spectral shift between excita-tion and emission frequencies [6]. In order to esti-mate the spectral intensity of Raman scattered light,three pieces of informationmust be known: the shapeand magnitude of the excitation energy spectrum,how that excitation energy is spectrally redistrib-uted, and some metric quantifying the “efficiency”of Raman scatter. The first two pieces are simplythe incident irradiance spectrum and the spectral re-distribution function, needed to predict the emissionspectra [7]. Therefore, most of the effort in ocean op-tics related to Raman scatter has centered on char-acterizing the third piece, the Raman scatteringcross section [8–11]. Gordon [12] provides a briefchronology of these measurements and how theycompare with various simulation [13–15] and field-based studies [16,17].

The results of these past efforts demonstrate thatRaman scattering can contribute significantly to themarine upwelling radiance field across all visiblewavelengths to a variable degree [8,14,17,18]. For ex-ample, Waters [15] carried out Monte Carlo simula-tions suggesting that the Raman fraction of waterleaving irradiance could be as high as ∼15%, but thiswas limited to longer wavelengths �λ > 650 nm�.Further, the effect decreased rapidly with increasingpigment biomass (∼2% when chlorophyll concentra-tion �Chl� � 1.0 mgm−3�. More recently, however,Gordon [12] modeled the Raman effect on the upwell-ing (ir) radiance and found it to be higher than pre-vious studies �> 25% of Lu�λ�, spectral upwellingradiance, in pure seawater for λ > 500 nm� and sig-nificant for chlorophyll concentrations up to5 mgm−3. Both of these results—a higher relativecontribution from Raman and a decreased depend-ence on Chl—were attributed to the use of revisedpure water absorption values [19] and newly re-ported spectral variability of the Raman scatteringcross section [10]. Gordon concluded that Ramanscattering “…cannot be ignored in ocean color mod-eling.” In subsequent work, Gordon et al. [20] alsodemonstrated that Raman scatter prevented opticalclosure efforts using hyperspectral radiometric fieldmeasurements. Thus, it should be evident thatRaman scatter can introduce uncertainty to modelsrelating the radiance field to the inherent opticalproperties (IOPs) of the ocean.

Despite the presumed importance of Ramanscattering, few studies have included it in semianalytical algorithms designed to invert in situ orsatellite ocean color reflectance data. In particular,three such algorithms have been put forward[21–23], but their implementation of Raman scatterhas not been carried forward in subsequent studiesor in the comprehensive report by the IOCCG [24].This may be due, in part, to the fact that ocean colorremote sensing satellites do not currently have ultra-violet (UV) bands, which are needed to computeRaman excitation in the blue part of the visible spec-trum. Indeed, these efforts have relied on empiricalrelationships or lookup tables derived from radiative

transfer simulations. Here, we present a simulateddataset to examine the effects of Raman scatteringon IOP inversion products from semianalytical mod-els. We then develop an approach to directly estimatethe inelastic Raman contribution to remote sensingreflectance and the resulting effects of its removalon inversion of simulated and satellite oceancolor data.

2. Methods

A. Radiative Transfer Simulations

A series of radiative transfer simulations (Hydro-Light, Sequoia Scientific, Inc.) were generated to(1) demonstrate the magnitude of the Raman effecton Rrs�λ� (remote-sensing reflectance, the ratio ofwater-leaving radiance to downwelling irradiancejust above the surface), and (2) provide a validationdataset for an approach to remove the Raman contri-bution to Rrs�λ�. Paired runs with and withoutRaman scatter were simulated for Chl rangingfrom 0.01 to 5.0 mgm−3 �Chl � 0.01; 0.02; 0.03; 0.04;0.07; 0.1; 0.2; 0.3; 0.5; 0.7; 1.0; 2.0; 5.0 mgm−3�. In or-der to efficiently incorporate Raman scattering intothe radiative transfer equation, HydroLight uses anazimuthally averaged formulation of Raman scatter,which gives the correct Raman contribution to irra-diances and nadir radiances (see Appendix A in [25]).The standard “Case 1” model embedded in Hydro-Light was used to relate Chl to other IOPs, detailsof which can be found in Gordon and Morel [26],Morel and Maritorena [27]. A fixed particle phasefunction (Fournier–Forand) was used with a particu-late backscattering ratio �bbp∕bp� equal to 0.01. Inthis model, pure seawater properties are specifiedby Pope and Fry [19] and Smith and Baker [28] forabsorption and scattering, respectively. For all simu-lations, a clear sky with solar zenith angle of 30° anda wind speed of 5 ms−1 was assumed.

B. Satellite Remote Sensing Data

Satellite products from two independent sensorswere used in this work, the ozone mapping instru-ment (OMI) on Aura and the MODerate-resolutionImaging Spectroradiometer (MODIS) on Aqua. BothAura and Aqua are part of the A-train constellationof Earth observing satellites, with Aura having anEquatorial crossing time just a few minutes laterthan Aqua (∼1∶30 pm). OMI data were obtained asdaily, Level 3 products from Goddard Earth SciencesData and Information Sciences Center (GES DISC),and were temporally binned to create monthly com-posites. These data consist of noon-time UV irradian-ces at four fixed wavelengths (305, 310, 324 and380 nm). From MODIS, monthly Level 3 productsof instantaneous PAR (iPAR) and spectral satelliteremote sensing reflectances,Rrs�λ�, were downloadeddirectly from the NASA Ocean Color Web portal(http://oceancolor.gsfc.nasa.gov/). iPAR was decom-posed to estimate spectral downwelling irradiance�Ed�λ�� using fixed fractions estimated from an

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atmospheric radiative transfer model [29]. Thefractional constants are stable within 1%–6% de-pending on wavelength and illumination conditions.Together, resultant Ed�λ� in the visible and OMI UVflux data allow pixel-wise reconstruction of incidentirradiance spectra. Ed�λ� at Raman excitation wave-lengths corresponding to MODIS visible bands (365,387.5, 421, 452.5, 467.5 nm for MODIS bands 8–12)were linearly interpolated and band-averaged (band-widths ∼10 nm). Global fields of MODIS Rrs�λ� wereused to estimate IOPs using two semianalytical in-version models; the Garver–Siegel–Maritorena(GSM) model [30] and the quasi-analytical algorithm(QAA) [31]. Retrieved IOPs include the phytoplank-ton absorption �aph�λ�, QAA only) or chlorophyllconcentration (Chl, GSM only), particulate backscat-tering coefficients �bbp�λ��, and dissolved and detritalorganic matter absorption coefficient �aCDM�λ��.C. Calculation of Raman Contribution to Remote SensingReflectance

We build on the approaches of Bartlett [18], Sathyen-dranath and Platt [22], and Loisel and Stramski [23]and express the remote sensing reflectance �Rrs� as

Rrs�λ; 0−� � Rrs;E�λ; 0−� �Rrs;IE�λ; 0−�; (1)

where the first term on the right-hand side accountsfor the contribution to Rrs from elastic scattering(subscript E), and the second term accounts for in-elastic scattering (subscript IE). For this exercise,we are functionally considering three distinct proc-esses as sources of “inelastic scattering” that affectremotely sensed ocean color; fluorescence from col-ored dissolved material (CDOM) and chlorophyll,and Raman scatter from seawater itself. However,CDOM fluorescence can be considered negligible[32], and chlorophyll fluorescence only impactsRrs near 685 nm [33]. Hence, we assume that atall wavelengths except near 685 nm:

Rrs�λ; 0−� � Rrs;E�λ; 0−� �Rrs;Raman�λ; 0−�: (2)

The immediate goal of semianalytical inversion al-gorithms is to obtain the spectral absorption andbackscattering coefficients for given Rrs;E�λ; 0−�of the surface ocean. Therefore, we must first esti-mate Rrs;Raman�λ; 0−� and remove it from measuredRrs�λ; 0−�. The Raman scattering coefficient, bR�λem�,accounts for light inelastically scattered from all rel-evant excitation wavelengths (λex) into an emissionwavelength, λem:

bR�λem� �Zλex

aR�λex�f R�λex → λem�dλex: (3)

Here, f R�λex → λem� is the wavelength redistributionfunction, which is normalized to unity over all emis-sion bands and whose shape was first described byWalrafen [7] for pure seawater. We follow the conven-tion of Mobley [34] and define the “Raman absorption

coefficient,” aR�λex�, which quantifies the loss ofradiant energy at the excitation wavelength due toinelastic Raman scatter. Bartlett et al. [10] providedthe most recent measurements of the Raman absorp-tion coefficient in seawater:

aR�λex� � 2.7 × 10−4�λex488

�−5.3

: (4)

Finally, the Raman scattered radiance in the upwarddirection (Lu;R) emanating from a subsurface layerbetween z1 and z1 � Δz at the emission band λem is

Lu;R�z1;Δz; λem�

� ~βR�θs → π�Z

z1

z1�Δz

Zλex

bR�λem�Ed�z; λex�e−Kdzdλexdz;

(5)

where ~βr�θs → π� is the Raman phase function,Ed�z; λex� is the downwelling irradiance at therelevant excitation wavelengths, and Kd is the at-tenuation coefficient of downwelling irradiance.Integrating over all depths and assuming verticallyhomogeneous optical properties and single scatter-ing, the Raman component of upwelling radiance justbeneath the sea surface equals

Lu;R�0−; λem� �~βr�θs → π�br�λem�Ed�0�; λex�

�Kd�λex� � κL�λem��: (6)

In this equation, κL�λem� is the attenuation coefficientfor upwelling radiance at emission wavelength λem,and both the Ed and Kd are averaged over all ex-citation bands (width less than 20 nm for visiblewavelengths<600 nm). For satellite applications, in-tegration of Lu;R�0−; λem� over the width of each sat-ellite band is required (∼10 nm for MODIS), which isapproximated by substituting band-averaged br andκL in Eq. (6). Similar expressions for the Ramancontribution to upwelled radiance have been derivedin previous studies [10,18,21,35,36].

Transmitting the radiance across the air–seainterface and normalizing to incident downwellingirradiance, Ed�0�; λem�, yields an equivalent remotesensing reflectance:

Rrs;Raman�0�; λem�

� t2

n2

~βr�θs → π�br�λem�Ed�0�; λex��Kd�λex� � κL�λem��Ed�0�; λem�

×�1� bb�λex�

μu�Kd�λex� � κ�λex�� bb�λem�

2μuκ�λem�

�: (7)

The additional terms in brackets on the right-handside of Eq. (7) account for higher orders of scattering(e.g., Raman scattered light in the downwarddirection, then elastically backscattered into theupwelling stream) and are derived in detail else-where [18,22].


In practice, the approach presented in Eq. (7) forestimating the Raman component of Rrs�λ� requiresestimates of IOPs (a and bb) and diffuse attenuation(K-functions). Therefore, an initial semianalyticalinversion must be made to provide an estimate ofthe total absorption and backscattering coefficients.Attenuation coefficients are then calculated as

Kd�λ� �a�λ� � bb�λ�

μdand κ�λ� � a�λ� � bb�λ�

μu; (8)

μd and μu are the mean cosine of downwelling andupwelling light, respectively, and the latter is setas 0.5 as the light field is assumed similar to thatof isotropic light [22], and the mean cosine fordownwelling irradiance is calculated followingGordon [37] and Lee et al. [38].

The semianalytical inversion models used here re-quire specification of eigenfunctions describing thespectral shape of IOPs. Therefore, another consider-ation that arises is extension of the eigenfunctions tothe UV region where UV irradiance excites Ramanemission in the visible. CDOM absorption and par-ticulate backscattering can be extrapolated to theUV with simple exponential or power laws thatadequately capture their spectral behavior (e.g.,[27]). Absorption by phytoplankton in the UV is morecomplicated and variable, as UV absorbing substan-ces of phytoplankton (e.g., mycosporine-like aminoacids) can vary independently of other pigments(e.g., [39,40]). Here, we assume that aph for λ <412 nm is spectrally flat, which may reflect a “mean”spectrum (see [40]).

3. Results

A. Results from Forward Simulations

Output from radiative transfer calculations provide acomplete and exact IOP/AOP dataset to developand test the approach for estimating the Raman

component of Rrs�λem� outlined in the previous sec-tion. Figure 1(a) shows simulated reflectance spectraover a wide range of Chl with and without Ramanscattering included (red dotted and black solidlines, respectively). The contribution from Ramanscattered light can be assessed as the ratio ofRrs;R�λ�∕Rrs�λ�, which increases with increasingwavelength, and with decreasing pigment concentra-tion [Fig. 1(b)]. Specifically, the presence of Ramanscatter enhances Rrs by 10% or less for λ < 500 nm,while at longer wavelengths Raman scattered lightcan account for nearly 25% of the total Rrs in theclearest waters [Fig. 1(b)]. Importantly, Rrs;R�λ� isnot spectrally flat, particularly in the blue to greenspectral region. The magnitudes of the Raman con-tribution to reflectance shown here are consistentwith previous studies (e.g., [12]) and are also a weakfunction of solar geometry and cloudiness.

B. Inversion Using Semianalytical Models

The simulated Rrs�λ� can be used as input to semian-alytical inversion models for estimation of IOPs inthe presence or absence of Raman scatter. In thiswork, we have chosen to use the GSM [30] andQAA [31] models, two approaches currently usedby NASA to produce satellite evaluation products.

Thesemodels returnvarious component absorptionand backscattering properties. QAA provides esti-mates of phytoplankton absorption at 443 nm,aph�443�, while GSM provides an estimate of Chl.Both models return absorption by colored dissolvedand detrital matter at 443 nm, aCDM�443�, and theparticulate backscattering coefficient at 443 nm,bbp�443�. Inversion results using the simulated reflec-tances are shown in Fig. 2. Biases exist in allretrieved parameters due to differing bio-opticalrelationships specified in the forward simulations(HydroLight) versus those assumed in the GSMand QAA inversion models. These differences couldbe easily reconciled by using the same expressions

Wavelength (nm)

low Chl

high Chl

low Chl

high Chl

Rrs

(sr

-1)

Rrs

,R :

Rrs(x

100)

(a)

(b)

Fig. 1. Spectral remote sensing reflectance fromHydroLight simulations. (a)Rrs�λ� for varying Chl for cases which include Raman scatter(dotted red lines) and which do not include Raman scatter (solid black lines). (b) Percent contribution of Raman scatter to Rrs�λ� expressedas the ratio of Rrs;R�λ�:Rrs�λ� times 100. Details of simulations are described in Section 2.


for phytoplankton, dissolved and detrital absorption,and particulate backscattering in the forward and in-verse models (not shown). However, it is the relativedifference in retrieved IOPs due to Raman scatterthat we focus on in this work. The relative error (orbias) is defined as �IOPuncorr–IOPcorr�∕IOPcorr � 100,where IOP is any retrieved IOP and the subscriptsuncorr and corr refer to IOPs estimated from reflec-tance spectra that are uncorrected or corrected forRaman, respectively. As a control, simulated spectrawith and without Raman scattering explicitly in-cluded are substituted in place of uncorrected and cor-rected reflectances, respectively. Results from thesecontrol runs (black lines in each panel of Fig. 3 showsthat (1) the relative error in each IOP due to Ramanscattering differs greatly between each IOP, (2) errorsdiffer between inversion models (GSM versus

QAA), (3) errors are greatest at low Chl and decreasewith increasing Chl, and (4) errors are greatest in theretrieval of bbp�443� [Figs. 3(a)–3(f)].Chl andaph�443�are overestimated by ∼15%–25% under the mostoligotrophic conditions �Chl < 0.02 mgm−3�, anddecrease to ∼5% when Chl > 0.3 mgm−3 [Figs. 3(a)and 3(d)]. Errors in aCDM�443� are negligible acrossall trophic conditions [Figs. 3(b) and 3(e)]. Errorsin bbp�443�, however, can be >100% under ultraoligo-trophic conditions and are still ∼20% when Chl >0.3 mgm−3 [Fig. 3(c)].

C. Evaluation of Raman Contribution Removal Scheme

The steps outlined in Section 2.C [Eq. (7)] result in anestimate of Rrs;R�λ�. We can provide a measure of val-idation for the approach using the simulated datasetby comparing estimates of Rrs;R�λ� with the absolute

aph(443) (m-1)

Chl (mg m-3)

Inve

rted

Chl

(m

g m

-3)

aCDM(443) (m-1) bbp(443) (m-1)

Inve

rted

aC

DM

(443

) (

m-1

)

Inve

rted

bbp

(443

) (

m-1

)

Inverted aph (443) ( m

-1)

(b)(a) (c)

Fig. 2. IOPs from inversion of HydroLight Rrs�λ�with and without Raman scatter included. Values plotted on the abscissae in each panelare taken from HydroLight and considered the “true” IOP value. (a) Chl from GSM (bottom and left axes) and aph�443� from QAA (top andright axes); (b) aCDM�443�; (c) bbp�443�. In each panel, “x” and “o” represent GSM and QAA retrievals, respectively. Red and blue symbolsrepresent inversions of Rrs�λ� with and without Raman scatter included, respectively.

Chl (mg m-3)

Bia

s (%

) in

Chl

Chl (mg m-3) Chl (mg m-3)

Bia

s (%

) in

aph

(443

)

Bia

s (%

) in

aC

DM

(443

)

Bia

s (%

) in

aC

DM

(443

)

Bia

s (%

) in

bbp

(443

)B

ias

(%)

in b

bp(4

43)

(b)(a) (c)

(f)(e)(d)

GSM

QAA

Fig. 3. Relative error in inverted IOPs due to Raman scatter as a function of chlorophyll concentration. Bias is calculated as normalizeddifference (%) between each retrieved IOP fromRrs�λ�with and without Raman scatter included. In each panel three curves are shown thatrepresent: error in retrievals using uncorrected Rrs (black line), error in retrievals after correction of Rrs with exact IOPs (blue line), anderror in retrievals after correction of Rrs with estimated IOPs from either GSM or QAA (red lines) IOPs in the top and bottom row,respectively. (a) GSM Chl; (b) GSM aCDM�443�; (c) GSM bbp�443�; (d) QAA aph�443�; e, QAA aCDM�443�; and (f) QAA bbp�443�.


difference in Rrs�λ� taken from consecutive runs withand without Raman scattering included �ΔRrs�(Fig. 4). In the best case scenario, exact IOP inputsfrom HydroLight can be used to estimate Rrs;R�λ�and the resultant agreement with ΔRrs is very goodacross the whole range of anticipated Rrs and over allvisible satellite wave bands r2 � 0.95, slope � 1.08,mean bias � 19%). When Rrs;R�λ� is estimated usinginverted IOPs rather than those taken directly fromHydroLight, predictability is slightly degraded withdifferences depending upon which inversion model is

used (red versus blue dots in Fig. 4). For example,application of GSM IOPs results in good linearcorrelation �r2 � 0.93�, but with a tendency tounderpredict ΔRrs (slope � 0.82, mean bias � 43%).If QAA IOPs are used to estimate Rrs;R�λ� thepattern is similar, but with slightly greater tendencyto underestimate ΔRrs (r2 � 0.94, slope � 0.69,mean bias � 50%).

Correction of Rrs for Raman scattering based uponIOPs from an initial inversion does not remove asmuch of the bias in each retrieved IOP as when exactHydroLight IOP input is used (compare red and bluelines in each panel of Fig. 3). For example, at lowChl�< 0.3 mgm−3� biases in aph�443� (QAA) andChl�GSM� of approximately 12% and 7% remain, re-spectively. Biases in aCDM�443� for both inversionmodels change by only a few percent upon correctionfor Raman, but are only a few percent even withoutcorrection. The largest changes between IOPs beforeand after correction for Raman are found in bbp�443�retrievals [Figs. 3(c) and 3(f)]. Large reductions inbias are achieved for QAA and GSM bbp�443�, butsignificant errors are still present, particularly atlower Chl concentrations. In the most oligotrophicexamples �Chl < 0.03 mgm−3� Raman bias >40%is still unaccounted for by the existing correction(see Discussion).

D. Application to Remote Sensing Data

Figure 5 shows the Raman contribution to Rrs�λ� fora single monthly composite of MODIS data fromOctober 2004. Results are shown for all MODIS

∆Rrs (sr-1)

Rrs

,R (

sr-1

)

Fig. 4. Estimation of Raman component of Rrs�λ�. Rrs;R is directlyestimated from Eq. (7). ΔRrs is the arithmetic difference betweenradiative transfer simulations with and without Raman scatteringincluded. Results for all visible satellite wave bands are shown to-gether. Diagonal line is 1:1 line.

Rrs,R : R

rs (x100)

Rrs,R : R

rs (x100)

Rrs,R : R

rs (x100)

Rrs,R : R

rs (x100)

Rrs,R : R

rs (x100)

443 nm412 nm

488 nm 531 nm

547 nm

Fig. 5. Fractional contribution of Raman component to total Rrs�λ� calculated for a single L3 monthly MODIS composite image (October2004). Values are expressed as a percentage (%) and each panel shows different MODIS wave bands in the visible.


ocean visible wave bands, except in the red (667 and678 nm), where the contribution from Chl fluores-cence can be significant. Three general observationsare evident and are consistent with results from thesimulated data: (1) values range from <1% to 10%,(2) contributions from Raman increase at longerwavelengths, and (3) contributions from Raman tendto be a decreasing function of biomass. The latterpoint can be seen as higher relative contribution toRrs�λ� from Raman scatter in the oligotrophic gyresand lower values in productive high latitude watersand areas of strong upwelling (Fig. 5). Further, if theglobal data are binned into three broad Chl ranges,which can loosely be categorized as oligotrophic,

mesotrophic, and eutrophic (Chl < 0.05 mgm−3,0.1 < Chl < 0.5 mgm−3, and Chl > 1.0 mgm−3, re-spectively), we can collapse the spatial informationand look at results across all wave bands (Fig. 6).The spectral variability is similar to that seen inthe simulated data presented in Fig. 1, where theRaman component contributes very little (∼2%) toRrs at 412 nm, but then increases more rapidly forclearer water. Maximal Rrs;R∕Rrs is observed at547 nm (formerly referred to as 551 nm) amongthe bands analyzed here and is approximately11%, 7%, and 2% for oligotrophic, mesotrophic, andeutrophic waters.

Last, we remove the estimated Rrs;R�λ� from satel-lite Rrs�λ� and re-invert the global fields to provideRaman-corrected IOP estimates (Fig. 7). The globaldistribution of IOPs before and after correction showvaried responses. For the GSM model, median Chldecreases only slightly (∼8%) from 0.12 mgm−3 to0.11 mgm−3 after correction for Raman [Fig. 7(a)].Median phytoplankton absorption �aph�443�� esti-mated from the QAA decreases similarly (8%) follow-ing correction [Fig. 7(d)]. Retrievals of CDOM anddetrital absorption, aCDM�443�, are particularly in-sensitive to the presence of Raman scattering andonly change by <3% for either inversion model[Figs. 7(b) and 7(e)]. The largest differences resultingfrom the Raman correction are observed in bbp�443�,similar to that seen in the simulated dataset. Globaldistributions of bbp�443� from GSM and QAA, precor-rection and postcorrection are shown in Figs. 7(c) and7(f). The distributions for each model are shifteddownward after Raman correction, and the overalldistributions become flatter. The changes inbbp�443� are further examined in Fig. 8, which shows

Chl < 0.05 mg m-3

Chl >1.0 mg m-3

0.1<Chl < 0.5 mg m-3

Wavelength (nm)

Rrs

,R :

Rrs

(x1

00)

Fig. 6. Fractional contribution of Raman scattered radiance tototal Rrs�λ� for various ranges of observed satellite Chl (October2004). Chl bins are for values <0.05 mgm−3 (top curve), 0.1 <Chl < 0.5 mgm−3 (middle curve), and Chl > 1.0 mgm−3 (bottomcurve). Error bars represent ranges of variability within eachChl bin. Results for MODIS wave bands >551 nm not shown,due to contamination by Chl fluorescence.

Chl (mg m-3) aCDM(443) (m-1) bbp(443) (m-1)

aph (m-1) aCDM(443) (m-1) bbp(443) (m-1)

GSM

QAA

(a) (b) (c)

(f)(e)(d)

Fig. 7. Histograms of global IOP retrievals for a single L3 monthly composite (October 2004). Top panels show GSM retrievals of (a) Chl;(b) aCDM�443�; (c) bbp�443�. Bottom panels show QAA retrievals for (d) aph�443�; (e) aCDM�443�; (f) bbp�443�. In each panel, the black histo-gram is from monthly values estimated without any correction for Raman scattering (the default), and the red line is from inversion afterremoving the Raman contribution to Rrs�λ�.


the overall distribution of the difference due toRaman correction (expressed as a relative bias, %),as well as the spatial distribution of this bias.Differences are consistently higher for GSMbbp�443� retrievals [Fig. 8(a)] than for the QAA.Raman correction results in values that are muchlower across most of themid-latitudes, and to a lesserextent at high latitudes. The median bias is ∼30%and 20% for the GSM and QAA, respectively, andsuggests that bbp�443� is significantly overestimatedover much of the ocean when using either model.While these “average” biases may not seem too largeon their own, it is important to note that up to 30% ofthe ocean has errors due to Raman in excess of 50%[see CDF in Fig. 8(c)].

4. Discussion and Conclusions

Failure to account for Raman scattering can lead tolarge errors in some semianalytically inverted prop-erties (e.g., particulate backscattering). Here, wehave developed a straightforward approximationfor the contribution of Raman scattering to remotesensing reflectance in satellite ocean color wavebands (e.g., MODIS). This method can be applied inconjunction with inversion of ocean color reflectancedata to yield more accurate IOPs which are relatedonly to the elastically backscattered component ofRrs�λ�. In addition to the observed Rrs�λ�, the only ex-ternal inputs that are required are spectral irradi-ance in the Raman excitation and emission bands,Ed�λex� and Ed�λem�. These values can be obtaineddirectly from a solar irradiance model (e.g., [41]) withknowledge of atmospheric properties, such as thatcarried out for operational ocean color processing.As an example in the work presented here, we haveused combined irradiance data in the UV regionfrom the OMI sensor with spectrally decomposed

irradiances in the visible which are derived fromthe standard MODIS iPAR product.

The approach presented here is not without itslimitations, and significant biases due to Raman re-main in inverted quantities even after correction.However, nearly all of the error due to Raman scattercan be corrected for, and removed if all inherent andapparent optical property input data is known accu-rately, such as the example shown with simulateddata (blue lines in Fig. 3). This suggests that inabilityto completely correct for the Raman scattering is notdue to the method presented in Eq. (7), but rather tothe inversion schemes themselves. Conceptually, thisprocedure should be run iteratively, with each itera-tion removing slightly more Raman-associated bias.What we found in doing so, however, is that the ex-ercise converged after a single iteration. Inspectionof Eqs. (7) and (8) show that the IOPs required toestimate Rrs;R�λ� are total absorption, a�λ�, and back-scattering, bb�λ�. Since a�λ� ≫ bb�λ� in the oligotro-phic ocean, Rrs;R�λ� is primarily dependent upontotal absorption, which is retrieved relatively well,particularly when including pure seawater absorp-tion. So, while errors in bbp�λ� may remain relativelylarge, the correction cannot improve them with sub-sequent iterations. Similar findings were reported byLoisel and Stramski [23]. Interestingly, inversion es-timates of aCDM�443� are relatively insensitive to thepresence of Raman and its correction. This is mostlikely because aCDM�λ� is weighted toward shortwavelengths (UV and blue/violet) and there is verylittle inelastic contribution to Rrs�λ� in this region(Fig. 1). This, in turn, results from the stronglyattenuated excitation irradiances for these emissionbands at the sea surface (peak excitation wave-lengths for the 412 and 443 nm MODIS bands areat ∼365 and 387 nm, respectively).

Bias (%

)

Bias (%

)

Bias (%) Bias (%)

(b)(a)

(c) (d)

Fig. 8. Comparison of satellite bbp�443� inversions before and after removal of Raman component of remote sensing reflectance, Rrs;R�λ�.(a) and (b) show the spatial distribution of error in bbp�443� due to Raman for the GSM and QAA inversions, respectively. (c) and (d) arehistograms of each respective image. Black lines are cumulative distribution functions of each field. Bias is calculated as normalizeddifference between bbp�443� estimated from satellite Rrs�λ� with and without Raman scatter included (×100 to express as a percentage).


There are other confounding factors for unravelingthe effect of Raman scattering on ocean color inver-sion models. For example, field data that is used toparameterize models (e.g., NASA’s NOMAD, [42]) al-ready contain inelastic scattering contributions fromRaman. The process of optimizing the inversion mod-els [27,31] should mitigate some of the Raman effect,such that errors estimated here may be viewed asupper bounds. Further, if inversion model coeffi-cients have been optimized to match Rrs containingRaman with coincident IOPs, then subsequent re-moval of the Raman component will necessarily de-grade the model’s ability to correctly retrieve theIOPs. In this context, a more appropriate test forRaman effects on inversionmodels would be to evalu-ate the retrieval of IOPs from corrected Rrs with amodel that has been “re”-optimized with a datasetthat has had Raman contributions to Rrs removed.

Alternative approaches that employ varying de-grees of complexity exist to correct Rrs�λ� for Ramanscattering (e.g., [22,23,43,44]). For inversion models,such as the GSM, which rely on a minimizationscheme, the Raman terms could simply be includedexplicitly within the inversion. Doing so may providea more compact, “eloquent” approach, but there is noreason to expect any different results from those pre-sented here. For models such as the QAA, this wouldnot be possible without significant reworking of themodel. A more common approach applicable to anyinversion scheme and which has been applied in pre-vious studies [23,43,44] draws directly from radia-tive transfer simulations. If a representative suiteof simulations with and without Raman scatter isgenerated, it is possible to construct a lookup tableor to parameterize Rrs;R�λ� as a function of environ-mental (e.g., Chl) or optical parameters (e.g., Rrs).This approach can work well, but is subject to limi-tations inherent in the radiative transfer model usedto generate the simulations (e.g., Case I-type as-sumptions). Further, it is not straightforward toevaluate how well this kind of approach works be-cause simulated data are again required to do so.In contrast, the approach presented here is free ofthese constraints, but the trade-off is that the correc-tion is limited by inaccurate IOP retrievals and theirextension to the excitation wavelengths as requiredto estimate Rrs;R�λ� via Eq. (7). Empirical “band-ratio” type algorithms for Chl [45] or diffuse attenu-ation [38,46], which are not examined here, may alsosuffer from biases due to Raman scatter.

The global patterns and conclusions drawn hereresult from the analysis of an illustrative exampleof a single monthly satellite composite. This ap-proach must be applied to a longer time period inorder to better characterize the extent of biasattributed to Raman scatter in the global ocean.The steep dependence of the Raman bias on Chl dic-tates how important it may be for a particular appli-cation. For example, regional studies in highlyproductive areas might ignore Raman effects withonly modest errors in retrieved IOPs. In contrast,

targeted studies of the oligotrophic gyres would bewell-served to consider Raman contributions toRrs�λ� and inverted IOPs. The results conveyed inFigs. 7 and 8 provide an illustrative example of globalpatterns. Last, the biases calculated must be propa-gated through to the biogeochemical quantities ofinterest to evaluate the significance of this process.For example, relationships that estimate particlestocks from bbp (e.g., [47,48]) will be affected in directproportion to the Raman bias. However, some appli-cations [e.g., calculation of net primary production(NPP)] will require more detailed sensitivity analy-ses to understand the impact of the Raman bias.

Funding for this work was provided by NASAgrant NNX12AJ13G to EB and TKW. The authorswish to thank Curtis Mobley for many helpful discus-sions in early stages of this work and comments on aprevious version of the manuscript. Two anonymousreviewers also greatly helped to improve the manu-script. Thanks also to Emmanuel Devred for sharingFortran code.

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